Apparatus, methods and storage medium for performing polarization-based quadrature demodulation in optical coherence tomography

ABSTRACT

Apparatus, method and storage medium which can provide at least one first electro-magnetic radiation to a sample and at least one second electromagnetic radiation to a reference, such that the first and/or second electromagnetic radiations have a spectrum which changes over time. In addition, a first polarization component of at least one third radiation associated with the first radiation can be combined with a second polarization component of at least one fourth radiation associated with the second radiation with one another. The first and second polarizations may be specifically controlled to be at least approximately orthogonal to one another.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is based upon and claims the benefit of priority fromU.S. Patent Application Ser. No. 60/708,271, filed Aug. 9, 2005, theentire disclosure of which is incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

The research leading to the present invention was supported, at least inpart, by National Institute of Health, Grant numbers R33 CA110130 andR01 HL076398. Thus, the U.S. government may have certain rights in theinvention.

FIELD OF THE INVENTION

The present invention relates to apparatus, methods and storage mediumfor processing signals based on optical coherence tomography techniques,and more particularly to a demodulation of Fourier-Domain opticalcoherence tomography signals usable for high-resolution cross-sectionalimaging of turbid, semi-turbid, and transparent samples, includingvarious biological samples.

BACKGROUND INFORMATION

Optical coherence tomography (“OCT”) techniques generally providescross-sectional images of biological samples with a resolution on thescale of several to tens of microns. Conventional OCT techniques, suchas time-domain OCT (“TD-OCT”) techniques, can generally uselow-coherence interferometry procedures to achieve depth ranging withina sample. In contrast, Fourier-Domain OCT (“FD-OCT”) techniques can usespectral-radar procedures to achieve depth ranging within the sample.FD-OCT techniques allow higher imaging speeds dues to an improvedsignal-to-noise performance and an elimination of a mechanically-scannedinterferometer reference arm. A standard implementation of the spectralranging technique in the FD-OCT systems does not provide an ability todiscriminate between objects at positive and negative displacementsrelative to the interferometric path-matched depth. This likely depthdegeneracy (alternately referred to as complex conjugate ambiguity) maylimit the imaging depth within the sample to either positive or negativedepths (which may prevent depth ranging ambiguity), effectively reducingthe inherent imaging depth by a predetermined factor (e.g., a factor oftwo).

Depth degeneracy in the FD-OCT systems can result from the detection ofonly the real component of the generally complex interference fringebetween the sample arm and the reference arm. If the complexinterferogram is detected, the above-described depth degeneracy can beeliminated or at least reduced. Various demodulation techniques havebeen implemented to allow for a measurement of the complexinterferogram. Such conventional techniques include phase shiftingtechniques, fused 3×3 coupler demodulation techniques, andfrequency-shifting techniques. The phase shifting techniques generallyuse an active phase modulator element in the interferometer todynamically adjust the relative phase between the sample arm and thereference arm. Multiple interferograms at various phase shifts may bemeasured and combined to produce the complex interferogram. One of thedisadvantages of this conventional technique is that the interferogramsare measured successively in time. This type of measurement reduces thesystem imaging speed, and allows for phase-drifts in the interferometerto degrade the measurement accuracy. The fused 3×3 couplers can yieldinterferograms on each of the 3 output ports that are phase-shiftedrelative to one another. The phase shift may depend on the couplingratio. For example, these outputs can be detected and recombined toyield the complex interferogram if the relative phase relationships areknown. High temperature, wavelength, and polarization sensitivity of thefused 3×3 (and in general fused N×N) coupler is used in a limited mannerin many interferometer demodulation schemes as requiring an accuratedemodulation. Conventional frequency shifting techniques have beensuccessfully applied to optical frequency domain imaging systems.However, these techniques are not know to have been used in the SD-OCTsystems. One of the reasons therefor is that such frequency shiftingtechniques usually utilize active elements, and have potentially limitedoptical bandwidths. Further, these techniques are generally not directlycompatible with nonlinear triggering to remove source sweepnonlinearities.

Accordingly, there is a need to overcome the deficiencies as describedherein above.

OBJECTS AND SUMMARY OF EXEMPLARY EMBODIMENTS

To address and/or overcome the above-described problems and/ordeficiencies, exemplary embodiments of systems, methods and softwarearrangements in accordance with the present invention are provided forperforming all-optical, passive, quadrature demodulation of the FD-OCTinterferometric outputs. Particular optical elements can be utilized tooptically create quadrature components of a complex interferogram.Detection and appropriate recombination of these quadrature outputs canallow measurement of the complex interferogram. As such, the exemplaryembodiments of the present invention facilitate the elimination or atleast a reduction of image range limitations due to the depthdegeneracy.

When used in an optical frequency domain imaging (“OFDI”) system, theexemplary embodiments of the present invention allow for both apolarization-diversity detection and a balanced-detection for a removalor a reduction of a source intensity noise. The exemplary embodiments ofthe present invention can be combined with nonlinear triggering so as tofacilitate, e.g., a substantial reduction of post-processingrequirements, which may be important for high-speed imaging.

When used with the SD-OCT system, the exemplary embodiments of thepresent invention facilitate an increase (e.g., a doubling) of theimaging depth range.

Thus, in accordance with one exemplary embodiment of the presentinvention, an apparatus, method and storage medium which can provide atleast one first electromagnetic radiation to a sample and at least onesecond electromagnetic radiation to a reference, such that the firstand/or second electromagnetic radiations have a spectrum which changesover time. In addition, a first polarization component of at least onethird radiation associated with the first radiation can be combined witha second polarization component of at least one fourth radiationassociated with the second radiation with one another. The first andsecond polarizations may be specifically controlled to be at leastapproximately orthogonal to one another.

In addition, at least one signal derived from an interference betweenthe first and second polarization components can be detected. The signaland/or the further signal may be modified into a first modified signaland/or a second modified signal, respectively, as function ofpredetermined data. A plurality of signals which are the signal and/orthe further signal can be obtained, statistical characteristics of theplurality of signals can be determined, and the predetermined data maybe derived based on the statistical characteristics.

According to another exemplary embodiment of the present invention, adifference of a phase of the first and second modified signals can becloser to approximately np+p/2 than a difference between a phase of thesignal and/or the first signal, where n is an integer and greater thanor equal to 0. Phases of the interference and the further interferencemay be substantially different from one another. A difference of phasesof the interference and the further interference may be substantiallynp+p/2, where n is an integer and greater than or equal to 0. The fourthradiation and at least a portion of the third radiation may have atleast one delay with respect to one another, and an image can beproduced as a function of the delay, the signal and the further signal.The delay may include at least one positive section and at least onenegative section, and a distinction can be made between at leastportions of the image that have positive and negative sections. The signand magnitude of the delay can be measured.

According to yet another exemplary embodiment of the present invention,an arrangement, method and storage arrangement can provide at least onefirst electro-magnetic radiation to a sample and at least one secondelectromagnetic radiation to a reference, such that the first and/orsecond electromagnetic radiations have a spectrum which changes overtime. In addition, a first signal can be generated as a function a firstinterference between at least one third radiation associated with thefirst radiation and at least one fourth radiation associated with thesecond radiation, and a second signal as a function a secondinterference between the third radiation associated and the fourthradiation. The first and second interferences can be different from oneanother. An arrangement which has a birefringence associated therewithcan be provided for specifically controlling, as a function of thebirefringence, a difference in phases of the first and secondinterferences to exclude np, where n is an integer and greater than orequal to 0.

These and other objects, features and advantages of the presentinvention will become apparent upon reading the following detaileddescription of embodiments of the invention, when taken in conjunctionwith the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the invention will becomeapparent from the following detailed description taken in conjunctionwith the accompanying figures showing illustrative embodiments of theinvention, in which:

FIG. 1 a is a block diagram of an exemplary embodiment of an FD-OCTsystem schematic;

FIG. 2 is a block diagram of an exemplary embodiment of apolarization-based demodulation optical arrangement which usesbulk-optic components in accordance with the present invention;

FIG. 3 is a block diagram of another exemplary embodiment of thearrangement of FIG. 2 modified to allow a balanced-detection for asource noise subtraction;

FIG. 4 is a block diagram of a further exemplary embodiment of thearrangement of FIG. 3 modified to allow both the balanced-detection andthe polarization-diversity detection;

FIG. 5 is a block diagram of another exemplary embodiment of an opticaldemodulation arrangement which can be functionally equivalent to thearrangement of FIG. 4 and modified to use most or all fiber-opticcomponents;

FIG. 6 is a block diagram of still another exemplary embodiment of theFD-OCT system in accordance with the present invention modified toincorporate a phase modulator used for calibration of any of theexemplary arrangements shown in FIGS. 2-5;

FIG. 7 is a flow diagram of an exemplary embodiment of an exemplarymethod according to the present invention for a calibration of theexemplary systems of the present invention and an operation of suchsystems;

FIG. 8 is a block diagram of one exemplary implementation of an OFDIsystem according to the present invention which can use any of theexemplary demodulation optical arrangements according to the presentinvention;

FIGS. 9A-9D are graphs of exemplary resulting measured A-lines receivedfrom the exemplary system of FIG. 8;

FIG. 10A is a graph of an exemplary measured axial point spread functionshown with and without the chirped clock;

FIG. 10B is a graph of an exemplary voltage-controlled oscillator(“VCO”) drive waveform for an unchirped (e.g., constant voltage curve)clock and a chirped clock; and

FIGS. 11A and 11B are images of human skin with and without the use ofthe complex demodulation, respectively.

Throughout the figures, the same reference numerals and characters,unless otherwise stated, are used to denote like features, elements,components or portions of the illustrated embodiments. Moreover, whilethe subject invention will now be described in detail with reference tothe figures, it is done so in connection with the illustrativeembodiments. It is intended that changes and modifications can be madeto the described embodiments without departing from the true scope andspirit of the subject invention as defined by the appended claims.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Theory of Exemplary Embodiments of the Invention

Fourier-Domain OCT techniques generally achieve depth-ranging usingspectral-radar techniques in which reflections from a sample interferewith a reference beam, and the resulting interferogram can be measuredas a function of optical wavelength. An exemplary embodiment of anFD-OCT system in accordance with the present is shown schematically inFIG. 1. The exemplary system of FIG. 1 includes a source 100 thatgenerates an output which is split into a sample arm and a reference armby a coupler 105. The sample arm light can be directed to a sample to beimaged 130. A focusing lens 125 can be used to achieve high transverseresolution. Reflections from this sample are collected by the same fiberand returned through a second coupler 115 to an output coupler 110. Thereference arm light is input on the other port of this output coupler110. The interference is detected by a receiver 120 as a function ofwavelength. In an exemplary embodiment of an OFDI system in accordancewith the present invention, this receiver can be a single photoreceiverwhich detects the output as a function of time while a narrowband sourcesweeps its output wavelength as a function of time. In an exemplaryembodiment of an SD-OCT system in accordance with the present invention,such receiver can be a spectrometer, which records the power at manywavelength through the use of a grating in combination with a line-scancamera. For a reflection at depth z where z=0 corresponds to a zeropath-length mismatch between the sample arm light and reference armlight, the interference term of the receiver output as a function ofwavenumber k can be given by the following:S(k)∝P(k)√{square root over (R_(ref)R_(s))} cos(2zk+φ _(z))where P(k) is the source power, R_(ref) is the reference arm powertransmission including coupling losses from the source to the receiver,R_(s) is the power reflectance of the sample arm due to a reflection atdepth z, and φ_(z) is the phase of the sample arm reflectance.

The amplitude and depth of the reflection can be given by the magnitudeand frequency of the measured signal as a function of wavenumber.Fourier transformation (FT) of the detected fringe with appropriatesubtraction of the non-interferometric terms can yield the complexreflectivity as a function of depth, a(z),a(z′)=FT(S(k))

The sign of the depth position (sign of z) is encoded in the sign of theresulting frequency (positive frequency or negative frequency). BecauseS(k) is real-valued, it would be difficult to differentiate betweenpositive and negative frequencies. Thus, a reflectance at +z may not beable to be distinguished from a reflectance at −z. This is whatgenerates the depth degeneracy of Fourier-Domain OCT techniques. Adetection of quadrature outputs, e.g., interference signals phased at90° relative to each other, can remove this depth degeneracy. Considerthe detection of the quadrature components S_(Q)(k) and S_(I)(k),S_(Q)(k)∝P(k)√{square root over (R_(ref)R_(s))} cos(2zk+φ_(z))S_(I)(k)∝P(k)√{square root over (R_(ref)R_(s))} sin(2zk+φ_(z))from which the complex signal, {tilde over (S)}(k), can be formed as{tilde over (S)}(k)=S _(Q)(k)+iS _(I)(k)=P(k)√{square root over (R_(ref) R _(s))}e ^(i(2zk+φ) _(z) ⁾and the depth reflectivity ã(k) is given by the FT of this complexsignal,{tilde over (a)}(z′)=FT({tilde over (S)}(k)).

Because {tilde over (S)}(k) is complex, it is possible to differentiatebetween positive and negative frequencies, and as a result eliminate thedegeneracy between positive and negative depths. In conventional FD-OCTsystems, the image depth is limited to positive depths to preventdegeneracy/ambiguity between signals from positive and negative depths.The maximum imaging range in such conventional systems is limited byfringe washout which is a decrease in signal amplitude for increasingdepth. The imaging depth in the conventional FD-OCT systems is thenbetween z=0 and z=+z1. Using exemplary embodiments of complexdemodulation techniques in accordance with the present invention, thedepth degeneracy can be reduced or removed, which allows imaging tooccur from −z1 to +z1, thus providing twice the image depth range of theconventional FD-OCT systems.

Exemplary Embodiment of an Optical Demodulation Circuit/Arrangement

According to an exemplary embodiment of the present invention, anoptical circuit/arrangement can be provided for generating thequadrature signals S_(Q)(k) and S_(I)(k) usable for a complexdemodulation. FIG. 2 shows one such exemplary embodiment which isdirected to an optical demodulation circuit/arrangement. In thisexemplary circuit arrangement, a reference arm light is collimated bycollimating optics 415, and directed to a first port 420 b of apolarizing beamsplitter (“PBS”) 420. The polarization controller 401enables the reference arm light to be reflected to an output port 420 c.A sample arm 405 light generated by this exemplary circuit/arrangementis collimated by collimating optics 410, and directed to a second inputport 420 a of the PBS 420. The S-polarized light in the sample arm canbe directed to the output port 420 c. The combined reference and samplearm light propagate to a beamsplitter (e.g., non-polarizing) 425, whichcan split substantially equal portions of this light to the output ports425 a, 425 b. The light output on the port 425 a travels through a firstbirefringent element 430, and then to a polarizer 435 oriented such thatthe transmitted polarization state is normal to the plane of the image.The light is then collected by an output fiber 460 through focusingoptics 450. This collected light is subsequently detected by a detector461 which can include a spectrometer adapted for a spectral-domain OCTsystem or a single photoreceiver adapted for an optical frequency domainimaging system. A similar analysis can be applied to the light whichexist the port 425 b, and which has access to a birefringent element (1)440 before the eventual detection thereof on via the detector 466.

The detected interference signal on output 2 for a single reflectance atposition z can be provided as:S ₂(k)≈B ₂(k)P(k)√{square root over (R_(ref)R_(s))} cos(2zk+φ_(z)+χ₂(k))where B₂(k), and χ₂(k) are functions of the birefringent element 2430.The output 1 on the fiber 465 can likewise be provided as:S ₁(k)≈B ₁(k)P(k)√{square root over (R_(ref)R_(s))} cos(2zk+φ_(z)+χ₁(k))where B₁(k), and χ₁(k) are functions of the birefringent element (1)440. An appropriate selection of the birefringent elements canfacilitate output signals with relative phase shift of 90°. For example,if the birefringent element (1) 440 is selected to be a quarter-waveplate oriented with its fast or slow axis at 45° relative to the vectornormal to the plane of the image, and the birefringent element (2) 430is selected to be a 45° Faraday rotator, then the phase differencebetween the outputs, χ₂(k)−χ₁(k), is approximately 90° and B₁(k)=B₂(k),thus providing the following:S ₁(k)≈S _(Q)(k)∝P(k)√{square root over (R_(ref)R_(s))} cos(2zk+φ _(z))S ₂(k)≈S ₁(k)∝P(k)√{square root over (R_(ref)R_(s))} sin(2zk+φ _(z))

It should be appreciated by those of ordinary skill in the art thatadditional combinations of the birefringent elements (1) and (2) can beused to generate quadrature signals, and that the orientations of thepolarizer 445, 435 can also be adjusted to produce the quadraturesignals. These signals may be combined post-detection to produce thecomplex interference signal in accordance with the present invention.

FIG. 3 shows another exemplary embodiment of the demodulation opticalcircuit/arrangement in accordance with the present invention that isconfigured to achieve a quadrature detection with a balanced-detectionfor a removal of source intensity noise as well as auto-correlationnoise from the sample. The operation is the arrangement of FIG. 3 issubstantially similar to that of FIG. 2 except that the polarizers ofFIG. 4 have been replaced by a polarizing beamsplitter (PBS) cubes 500,530. Both output ports of the PBS cubes 500 can be detected, and theirsignals are preferably subtracted in the balanced receiver. In thisexemplary configuration, the interference signal can be increased, andthe noise fluctuations from the noise may be subtracted. The output ofbalanced-receivers 525, 555 of this exemplary arrangement provide thequadrature interference signals to be combined to form the complexinterference signal.

FIG. 4 shows another exemplary embodiment of the optical circuitarrangement according to the present invention, which is a modificationof the arrangement of FIG. 3. In particular, the arrangement of FIG. 4allows for a detection of a polarization-diversity. The polarizationdiversity enables a detection of the interference fringe which canresult from the sample that ate are light in both polarizations. Thepolarization controller 600 of the arrangement of FIG. 4 can beconfigured to direct substantially equal portions of the reference armpower to both output ports of the first PBS 601. Each output port of thefirst PBS 601 detects the sample arm light arriving in a givenpolarization. The circuit 590 is substantially the same as the one shownin FIG. 3, and may be repeated on a fourth PBS output port 592. In thisexemplary configuration, outputs A and B describe one signalpolarization, and outputs C and D describe the other signalpolarization.

FIG. 5 shows another exemplary embodiment of the demodulation opticalcircuit/arrangement according to the present invention that may befunctionally equivalent or similar to the circuit/arrangement of FIG. 4,and constructed from fiber-optic components. For example, thebirefringent elements of FIG. 4 can be replaced by polarizationcontrollers 610 a, 615 a, 610 b, 615 b which are adjusted such thatquadrature signals are created on output ports 625 a and 625 b, andlikewise quadrature outputs can be generated on output ports 625 c and625 d.

In the exemplary configurations that utilize bulk-optic birefringentelements (as shown in FIGS. 2-4), the birefringence elements can beselected to generate quadrature components which are phase-shifted by90°. In the fiber-optic configuration of FIG. 5, the polarizationcontrollers may be adjusted while the interference fringes can bemonitored such that approximately a 90° phase shift is induced. Thedeviations in the phase shift from 90° can be measured and corrected foras described herein below.

Calibration

For example, the measured signals will not be exactly in quadrature andthus a calibration procedure must be used to create quadrature signalsfrom the measured signals. Assume that the measured signals are given byS _(Q)(k)=A _(Q)(k)+B _(Q)(k)cos(φ)S ₁(k)=A ₁(k)+B ₁(k)sin(φ+ζ((k))where φ is the interferometric phase difference containing thedepth-information. The parameters A_(Q), B_(Q), A_(I), B_(I), and ζ canbe determined by the source spectrum and demodulation circuit. If theparameters are known, exact quadrature signals can be constructed asfollows: $\begin{matrix}{{S_{Q}^{\prime} = {{B_{Q}{\cos(\phi)}} = {S_{Q} - A_{Q}}}}{S_{I}^{\prime} = {{B_{Q}{\sin(\phi)}} = \frac{{\left( \frac{B_{Q}}{B_{I}} \right)\left( {S_{1} - A_{1}} \right)} - {\left( {S_{Q} - A_{Q}} \right){\sin(\zeta)}}}{\cos(\zeta)}}}} & (1)\end{matrix}$where the explicit dependence on k of the parameters is not describedherein for the sake of clarity. A_(Q) and A_(I) can be measured usingeither of the following methods:

-   -   (a) The sample arm light is blocked, and the output can be        recorded as a function of k. Because the returned sample arm        power is much less than the reference arm power, A_(Q)(k) and        A_(I)(k) are determined by the detected reference arm power        without any interference; and/or    -   (b) The parameters A_(Q)(k) and A_(I)(k) can be measured by        record the signals with or without reflections from the sample        arm and taking the average over a significant number of        measurements. Because the interference terms averages to zero        due to interferometer drift, the average yields A_(Q),A_(I).        Alternatively, a phase modulator can be placed in the        interferometer in either the reference arm or sample arm. FIG. 6        illustrates such exemplary embodiment of the circuit/arrangement        which includes a phase modulator 700 that is placed in the        reference arm. This phase modulator 700 can be used to ensure        that the interferometer phase is randomized over the period of        time that A is being measured. If the phase modulation is much        less than π over the time period of one A-line, this phase        modulator 700 can remain active during imaging. Otherwise, it        should be turned off during the imaging procedure.

The ratio of B_(Q)(k) to B_(I)(k) can be measured by recording theoutput with a reflection in the sample arm, ideally with the phasemodulator 700 of FIG. 6 on, otherwise over a long enough time to ensurerandom distributions of phase. The ratio can be provided as follows:$\begin{matrix}{\left( \frac{B_{Q}}{B_{l}} \right)^{2} = \frac{\left\langle {\Delta\quad S_{Q}^{2}} \right\rangle}{\left\langle {\Delta\quad S_{I}^{2}} \right\rangle}} & (2)\end{matrix}$where${\left\langle {\Delta\quad x^{2}} \right\rangle = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {x_{i} - \overset{\_}{x}} \right)^{2}}}},$and the summation i is over samples at a given wavenumber k.

The parameter ζ can be calculated as follows: $\begin{matrix}{\frac{\left\langle {\Delta\left( {S_{Q} + S_{I}} \right)}^{2} \right\rangle - \left\langle {\Delta\quad S_{Q}^{2}} \right\rangle - \left\langle {\Delta\quad S_{I}^{2}} \right\rangle}{2\sqrt{\left\langle {\Delta\quad S_{Q}^{2}} \right\rangle\left\langle {\Delta\quad S_{I}^{2}} \right\rangle}} = {\sin(\zeta)}} & (3)\end{matrix}$

The exemplary embodiment of a procedure according to the presentinvention to perform such determination is shown in FIG. 7. Inparticular, in step 655, the polarization controllers (“PCs”) can beconfigured to provide output signal phased at approximately 90 degrees(if the fiber configuration of FIG. 5 is utilized). In step 660, signalsS_(Q)(k) and S_(I)(k) are measured, while reference arm position orphase is modulated. In step 665, the following is calculated:A_(Q)(k)=<S_(Q)(k)>, and A_(I)(k)=<S_(I)(k)>using formulas (2) and (3)above. These steps are performed during the system calibration. Thesteps described below are performed during the use of the system. Forexample, in step 670, signals S_(Q)(k) and S_(I)(k) are measured, and instep 675, the fringes are calculated using the equation (1). Then, instep 680, a complex signal S_(Q)′+sqrt(−1)*S_(I)′is constructed.

The exemplary embodiment of the system according to the presentinvention (e.g., of the exemplary OFDI system) is shown in FIG. 8. Forexample, the laser 700 output swept over 105 nm centered at 1325 nm canbe provided for the exemplary system. This exemplary source can be splitinto a sample arm 705 (e.g., 90%) and a reference arm 710 (e.g., 10%). Aportion of the reference arm light can be directed to a fiber Bragggrating (“FBG”) 715, thus generating a reflected optical pulse that isdetected and converted to a TTL trigger signal. The remainder of thereference arm light can pass through a variable optical delay (e.g.,used to path-length match the interferometer), and provided on one portof a fiber-pigtailed polarization beam combiner (“PBC”) 720. Thepolarization controller 725 (“PC”) in the reference arm 710 can be usedto maximize the coupling of the reference arm light to the PBC outputport. The reflected sample arm light is directed to the other input portof the PBC. One polarization state of this light can be coupled to thePBC output port. Following the PBC is the optical demodulation circuitthat uses polarization-based biasing to generate an in-phase signal,S_(I), and a quadrature signal, S_(Q), for each interference fringe.

In this manner, the complex interference signal (S_(I)+iS_(Q)) can beconstructed. Because the complex signal indicates the direction of phaseflow, it allows unambiguous discrimination between positive and negativeoptical delays and eliminates depth degeneracy. To illustrate thedemodulation circuit, the reference arm light and the sample arm lightcan be orthogonally polarized on the output port of the first PBC inFIG. 8, and thus the state of polarization of the light is modulatedinstead of the intensity. This light can be split by the 50/50 coupler730, and each output may be directed to a PC 735 a,735 b followed by apolarization beam splitter (PBS) 740 a,740 b that converts thepolarization modulation to intensity modulation. Arbitrarily, the signalfrom the upper path is defined as S_(I) and from the lower path asS_(Q). In each, path the polarization controllers 735 a, 735 b is set tosplit the reference arm light equally between the two output ports ofthe PBSs 740 a, 740 b, and the outputs are connected tobalanced-receivers 745 a,745 b to provide subtraction of intensitynoise. Within the constraint of equally splitting the reference armpower among the output ports, the phase of S_(I) and S_(Q) can bearbitrarily set by manipulation of the corresponding PC. In our system,a relative phasing of 90° between S_(I) and S_(Q) is likely induced.

Using the measured signals S_(I) and S_(Q) to directly form the complexinterference signal (e.g., without any correction post-detection) canresult in a moderate extinction between positive and negative depths.FIG. 9A shows a graph of a measured A-line of a stationary mirror at adepth of +1.7 mm calculated by the direct use of the measured signalsS_(I) and S_(Q). The resultant extinction shown in this graph is 30 dB.To improve the extinction, a corrected signal, Ŝ_(Q), can be calculatedfrom the measured signals S_(I) and S_(Q) using previously acquiredcalibration data that describes the state of the optical demodulationcircuit. The in-phase signal at a given wavenumber k may be given byS_(I)=B sin(φ), and that the quadrature signal is provided by S_(Q)=αBcos(φ−ε), where α and ε describe the deviation of S_(Q) from the truequadrature signal (α=1 and ε=0 for a true quadrature signal). It can beassumed that the DC component has been subtracted. A correctedquadrature signal Ŝ_(Q) to the measured in-phase signal S_(I) is givenbyŜ _(Q) ≡B cos(φ)=(α cos(ε))³¹ ¹ S _(Q) −tan(ε)S _(I).

A statistical method can be used to measure the parameters α and ε (allfunctions of wavenumber k) for a given setting of the opticaldemodulation circuit. Multiple interference fringes can be recorded inthe presence of a sample arm reflection while the reference arm positionis slowly displaced over a few microns with a piezo-translator. Theresulting dataset may contain signals S_(Q) and S_(I) at each wavenumberwith a quasi-randomized distribution in phase (φ) (due to the referencearm dithering). The calibration parameters can then be calculatedstatistically as follows: α = σ_(S_(Q))σ_(S_(I))⁻¹${\sin(ɛ)} = \frac{\sigma_{({S_{Q} - S_{I}})}^{2} - \sigma_{(S_{Q})}^{2} - \sigma_{(S_{Q})}^{2}}{2\sigma_{(S_{Q})}\sigma_{(S_{I})}}$where σ_(x) is the standard deviation (over sample number) of themeasured signal x and is a function of wavenumber. In these experiments,the reference mirror was translated by a few microns with a 30 Hztriangular waveform and signals were recorded over a time period of 3seconds at an A-line rate of 15.6 kHz. FIG. 9B shows same A-line as inFIG. 9A but using the corrected complex signal, (S_(I)+iŜ_(Q)). Theextinction is improved from 30 dB to greater than 50 dB. FIGS. 9C and 9Dshow A-lines measured at mirror depths of +0.4 mm and −1.3 mm. Each ofFIGS. 9B-9D used the same previously derived calibration parameters αand ε and achieve greater than 50 dB extinction. With properenvironmental shielding of the optical demodulation circuit, thecalibration coefficients remained valid over periods greater than 60minutes. The sensitivity of the system was measured to vary from 107 dBnear a depth of +0.2 mm to 103 dB at a depth of +2.0 mm.

To demonstrate chirped-clock sampling, a clock generator 750 (see FIG.8) using a voltage-controlled oscillator circuit. The output clockfrequency is controlled through an analog voltage input and can be sweptphase-continuously with a smoothly varying analog input waveform. Thiswaveform is generated by the data acquisition (DAQ) 765 electronics andis repeated for each sweep of the source. The waveform is triggered fromthe same trigger signal used for data acquisition and is thussynchronized to the source sweep. FIG. 10A shows the measured axialpoint spread function of a mirror located at a displacement ofapproximately −1.1 mm from the zero differential delay point using botha constant frequency clock signal and a chirped frequency clock signal.FIG. 10B shows the analog waveform input to the VCO clock circuit forboth the constant frequency and chirped frequency clock signals. Astraightforward iterative routine was used to set the find the optimalVCO analog waveform for a given configuration of the source. Thiswaveform remains valid until the source is reconfigured. Using thechirped frequency clock signal, the axial resolution of was measured tobe 13.5-14.5 μm in air and is transform limited across the full imagingdepth range.

Images of a human finger in-vivo acquired at an A-line rate of 15.6 kHzare shown in FIG. 11. The image size is 5 mm transverse by 4.3 mm depth(500×408). The depth resolution is 14 μm in air and the transverseresolution is 25 μm. The imaging frame rate is 30 fps. In FIG. 11A, theimage is generated based on only the in-phase signal SI, showing theeffect of depth-degeneracy. In FIG. 11B, the complex signal is used andthe depth-degeneracy artifacts are removed, allowing unambiguous imagingover 4.3 mm.

The foregoing merely illustrates the principles of the invention.Various modifications and alterations to the described embodiments willbe apparent to those skilled in the art in view of the teachings herein.Indeed, the arrangements, systems and methods according to the exemplaryembodiments of the present invention can be used with any OCT system,OFDI system, SD-OCT system or other imaging systems, and for examplewith those described in International Patent ApplicationPCT/US2004/029148, filed Sep. 8, 2004, U.S. patent application Ser. No.11/266,779, filed Nov. 2, 2005, and U.S. patent application Ser. No.10/501,276, filed Jul. 9, 2004, the disclosures of which areincorporated by reference herein in their entireties. It will thus beappreciated that those skilled in the art will be able to devisenumerous systems, arrangements and methods which, although notexplicitly shown or described herein, embody the principles of theinvention and are thus within the spirit and scope of the presentinvention. In addition, to the extent that the prior art knowledge hasnot been explicitly incorporated by reference herein above, it isexplicitly being incorporated herein in its entirety. All publicationsreferenced herein above are incorporated herein by reference in theirentireties.

1. An apparatus comprising: at least one first arrangement capable ofproviding at least one first electro-magnetic radiation to a sample andat least one second electro-magnetic radiation to a reference, whereinat least one of the first and second electro-magnetic radiations has aspectrum which changes over time; and at least one second arrangementcapable of combining a first polarization component of at least onethird radiation associated with the at least one first radiation and asecond polarization component of at least one fourth radiationassociated with the at least one second radiation with one another,wherein the first and second polarizations are specifically controlledto be at least approximately orthogonal to one another.
 2. The apparatusaccording to claim 1, further comprising at least one third arrangementcapable of detecting at least one signal derived from an interferencebetween the first and second polarization components.
 3. The apparatusaccording to claim 2, wherein the at least one third arrangement isfurther capable of detecting at least one further signal derived from afurther interference between the first and second polarizationcomponents.
 4. The apparatus according to claim 3, wherein the thirdarrangement is further capable of modifying at least one of the at leastone signal or the at least one further signal into at least one of afirst modified signal or a second modified signal, respectively, asfunction of predetermined data.
 5. The apparatus according to claim 4,wherein the predetermined data is obtained based on at least one of acharacteristic or a state of the third arrangement.
 6. The apparatusaccording to claim 3, wherein the third arrangement is further capableof obtaining a plurality of signals which are at least one of the atleast one signal or the at least one further signal, determiningstatistical characteristics of the plurality of signals, and derivingthe predetermined data based on the statistical characteristics.
 7. Theapparatus according to claim 4, wherein a difference of a phase of thefirst and second modified signals is closer to approximately nπ+π/2 thana difference between a phase of the at least one signal or the at leastone first signal, where n is an integer and greater than or equal to 0.8. The apparatus according to claim 3, wherein phases of theinterference and the further interference, respectively, aresubstantially different from one another.
 9. The apparatus according toclaim 3, wherein a difference of phases of the interference and thefurther interference, respectively, are substantially nπ+π/2, where n isan integer and greater than or equal to
 0. 10. The apparatus accordingto claim 3, wherein the fourth radiation and at least a portion of thethird radiation have at least one delay with respect to one another, andfurther comprising at least one fourth arrangement capable of producingan image as a function of the delay, the signal and the further signal.11. The apparatus according to claim 10, wherein the at least one delayincludes at least one positive section and at least one negativesection, and wherein the at least one fourth arrangement is capable ofdistinguishing between at least portions of the image that have positiveand negative sections.
 12. The apparatus according to claim 11, whereinthe at least one fourth arrangement is capable of measuring the sign andmagnitude of the at least one delay.
 13. An apparatus comprising: atleast one first arrangement capable of providing at least one firstelectro-magnetic radiation to a sample and at least one secondelectro-magnetic radiation to a reference, wherein at least one of thefirst and second electro-magnetic radiations has a spectrum whichchanges over time; at least one second arrangement capable of generatinga first signal as a function a first interference between at least onethird radiation associated with the at least one first radiation and atleast one fourth radiation associated with the at least one secondradiation, and a second signal as a function a second interferencebetween the at least one third radiation associated and the at least onefourth radiation, the first and second interferences being differentfrom one another; and at least one third arrangement which has abirefringence associated therewith, and capable of specificallycontrolling, as a function of the birefringence, a difference in phasesof the first and second interferences to exclude nπ, where n is aninteger and greater than or equal to
 0. 14. The apparatus according to13, wherein the at least one third arrangement includes at least one ofa fiber polarization controller and a bulk optic birefringentarrangement.
 15. A method, comprising: providing at least one firstelectro-magnetic radiation to a sample and at least one secondelectro-magnetic radiation to a reference, wherein at least one of thefirst and second electro-magnetic radiations has a spectrum whichchanges over time; and combining a first polarization component of atleast one third radiation associated with the at least one firstradiation and a second polarization component of at least one fourthradiation associated with the at least one second radiation with oneanother, wherein the first and second polarizations are specificallycontrolled to be at least approximately orthogonal to one another. 16.The method according to claim 15, further comprising detecting at leastone signal derived from an interference between the first and secondpolarization components.
 17. The method according to claim 16, furthercomprising detecting at least one further signal derived from a furtherinterference between the first and second polarization components. 18.The method according to claim 17, further comprising modifying at leastone of the at least one signal or the at least one further signal intoat least one of a first modified signal or a second modified signal,respectively, as function of predetermined data.
 19. The methodaccording to claim 17, further comprising obtaining a plurality ofsignals which are at least one of the at least one signal or the atleast one further signal, determining statistical characteristics of theplurality of signals, and deriving the predetermined data based on thestatistical characteristics.
 20. The method according to claim 17,wherein a difference of a phase of the first and second modified signalsis closer to approximately nπ+π/2 than a difference between a phase ofthe at least one signal or the at least one first signal, where n is aninteger and greater than or equal to
 0. 21. The method according toclaim 17, wherein phases of the interference and the furtherinterference, respectively, are substantially different from oneanother.
 22. The method according to claim 17, wherein a difference ofphases of the interference and the further interference, respectively,are substantially nπ+π/2, where n is an integer and greater than orequal to
 0. 23. The method according to claim 17, wherein the fourthradiation and at least a portion of the third radiation have at leastone delay with respect to one another, and further comprising producingan image as a function of the delay, the signal and the further signal.24. The method according to claim 23, wherein the at least one delayincludes at least one positive section and at least one negativesection, and further comprising distinguishing between at least portionsof the image that have positive and negative sections.
 25. The methodaccording to claim 24, further comprising measuring the sign andmagnitude of the at least one delay.
 26. A method comprising: providingat least one first electro-magnetic radiation to a sample and at leastone second electro-magnetic radiation to a reference, wherein at leastone of the first and second electro-magnetic radiations has a spectrumwhich changes over time; generating a first signal as a function a firstinterference between at least one third radiation associated with the atleast one first radiation and at least one fourth radiation associatedwith the at least one second radiation, and a second signal as afunction a second interference between the at least one third radiationassociated and the at least one fourth radiation, the first and secondinterferences being different from one another; and with an arrangementwhich has a birefringence associated therewith, specificallycontrolling, as a function of the birefringence, a difference in phasesof the first and second interferences to exclude nπ, where n is aninteger and greater than or equal to
 0. 27. A storage medium which hassoftware provided thereon, wherein the software is capable of beingexecuted by a processing arrangement to perform the steps comprising:providing at least one first electro-magnetic radiation to a sample andat least one second electro-magnetic radiation to a reference, whereinat least one of the first and second electro-magnetic radiations has aspectrum which changes over time; and combining a first polarizationcomponent of at least one third radiation associated with the at leastone first radiation and a second polarization component of at least onefourth radiation associated with the at least one second radiation withone another, wherein the first and second polarizations are specificallycontrolled to be at least approximately orthogonal to one another.
 28. Astorage medium which has software provided thereon, wherein the softwareis capable of being executed by a processing arrangement to perform thesteps comprising: providing at least one first electro-magneticradiation to a sample and at least one second electro-magnetic radiationto a reference, wherein at least one of the first and secondelectro-magnetic radiations has a spectrum which changes over time;generating a first signal as a function a first interference between atleast one third radiation associated with the at least one firstradiation and at least one fourth radiation associated with the at leastone second radiation, and a second signal as a function a secondinterference between the at least one third radiation associated and theat least one fourth radiation, the first and second interferences beingdifferent from one another; and using an arrangement which has abirefringence associated therewith, specifically controlling, as afunction of the birefringence, a difference in phases of the first andsecond interferences to exclude nπ, where n is an integer and greaterthan or equal to 0.